Mapping Species Distributions with MAXENT Using a ...

Mapping Species Distributions with MAXENT Using aGeographically Biased Sample of Presence Data: APerformance Assessment of Methods for CorrectingSampling BiasYoan Fourcade1*, Jan O. Engler2,3, Dennis Rodder3, Jean Secondi1

1 LUNAM Universite d’Angers, GECCO (Groupe ecologie et conservation des vertebres), Angers, France, 2 Department of Wildlife Ecology, University of Gottingen,

Gottingen, Germany, 3 Zoological Research Museum Alexander Koenig, Bonn, Germany

Abstract

MAXENT is now a common species distribution modeling (SDM) tool used by conservation practitioners for predicting thedistribution of a species from a set of records and environmental predictors. However, datasets of species occurrence usedto train the model are often biased in the geographical space because of unequal sampling effort across the study area. Thisbias may be a source of strong inaccuracy in the resulting model and could lead to incorrect predictions. Although anumber of sampling bias correction methods have been proposed, there is no consensual guideline to account for it. Wecompared here the performance of five methods of bias correction on three datasets of species occurrence: one ‘‘virtual’’derived from a land cover map, and two actual datasets for a turtle (Chrysemys picta) and a salamander (Plethodoncylindraceus). We subjected these datasets to four types of sampling biases corresponding to potential types of empiricalbiases. We applied five correction methods to the biased samples and compared the outputs of distribution models tounbiased datasets to assess the overall correction performance of each method. The results revealed that the ability ofmethods to correct the initial sampling bias varied greatly depending on bias type, bias intensity and species. However, thesimple systematic sampling of records consistently ranked among the best performing across the range of conditionstested, whereas other methods performed more poorly in most cases. The strong effect of initial conditions on correctionperformance highlights the need for further research to develop a step-by-step guideline to account for sampling bias.However, this method seems to be the most efficient in correcting sampling bias and should be advised in most cases.

Citation: Fourcade Y, Engler JO, Rodder D, Secondi J (2014) Mapping Species Distributions with MAXENT Using a Geographically Biased Sample of Presence Data:A Performance Assessment of Methods for Correcting Sampling Bias. PLoS ONE 9(5): e97122. doi:10.1371/journal.pone.0097122

Editor: John F. Valentine, Dauphin Island Sea Lab, United States of America

Received March 3, 2014; Accepted April 14, 2014; Published May 12, 2014

Copyright: � 2014 Fourcade et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permitsunrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Funding: This study was supported by a grant to YF and JS from Plan Loire Grandeur Nature and European Regional Development Fund (ERDF). JOE was kindlysupported within the German Federal Environmental Foundation fellowship program. The funders had no role in study design, data collection and analysis,decision to publish, or preparation of the manuscript.

Competing Interests: The authors have declared that no competing interests exist.

* E-mail: [email protected]

Introduction

A key issue in ecology and conservation biology is to determine

how species are distributed in space. Since extinction risk is

associated with range size [1], a significant reduction of a species

range often determines change in conservation status (see for

example IUCN criteria [2,3]) and prime conservations actions

[4,5]. Likewise, protected areas usually focus on biodiversity

hotspots [6] in order to conserve efficiently as many species as

possible [7–9]. Therefore, conservationists often need precise

assessments of species ranges. Beyond simple range description,

identifying which main factors limit distributions is essential to

efficiently forecast the benefits of conservation management. In

order to deal with these questions, several methods of species

distribution modeling (SDM), also known as ecological niche

modeling (ENM) [10], have been developed since the 1980s [11].

The principle of SDM is to relate known locations of a species

with the environmental characteristics of these locations in order

to estimate the response function and contribution of environ-

mental variables [12], and predict the potential geographical range

of a species [13]. These models estimate the fundamental

ecological niche in the environmental space (i.e. species response

to abiotic environmental factors [14]) and project it onto the

geographical space to derive the probability of presence for any

given area or, depending on the method, the likelihood that

specific environmental conditions are suitable for the target species

[15]. Distribution models are used by conservation practitioners to

estimate the most suitable areas for a species and infer probability

of presence in regions where no systematic surveys are available

[16]. They can also assess the potential expansion of introduced

species in newly colonized areas [17,18], estimate the future range

of a species under climate change [18,19] or assist in reserve

planning [20].

Several statistical models exist to predict the distribution of a

species [21]. Beyond classical regression methods (Resource

Selection Function RSF [22,23], Generalized Linear Models

GLM [24]), algorithmic modeling based on machine learning (for

example Artificial Neural Networks [25], Maximum Entropy

MAXENT [26], Classification And Regression Trees CART [27])

have become increasingly popular in recent years. Among these,

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MAXENT has been described as especially efficient to handle

complex interactions between response and predictor variables

[15,28], and to be little sensitive to small sample sizes [29]. This, as

well as its extreme simplicity of use, has made MAXENT the most

widely used SDM algorithm. In December 2013, 1886 citations of

the article describing the method [30] were reported in Web of

Science.

MAXENT modeling, and SDM in general, is now commonly

implemented in conservation-oriented studies [31]. Regional or

continent-wide studies are facilitated by the recent availability of

global datasets. Environmental layers, such as the global climate

variables developed in the WorldClim project [32], offer

continuous description of very large areas [33]. Similarly, the

development of open biodiversity databases (see for example the

Global Biodiversity Information Facility, GBIF, http://www.gbif.

org) increases manifolds the spatial coverage of fieldwork

observations that could have been collected by a single project.

Such databases usually provide presence-only data that can be

handled by modeling methods like MAXENT.

However, datasets derived from opportunistic observations or

museum records rather than from planned surveys often exhibit a

strong geographic bias [34], some areas being visited more often

than others because of their accessibility [35] or their naturalistic

interest. This unequal survey coverage of a species distribution is

often referred as sampling bias, sample selection bias or survey

bias. The quality of the model can be strongly affected if entire

parts of the environmental space suitable to a species are absent or

poorly represented in the survey dataset [36,37], or alternatively, if

some areas are overrepresented due to locally high sampling

efforts. Several studies questioned the effect of sampling design

[38], or the biased nature of museum and herbarium datasets [39]

on the predictive performance of SDMs. Surprisingly, the issue of

quantifying and correcting sampling bias has been poorly

addressed despite its crucial importance. Although authors pointed

out that the distribution of locations in the geographical and/or

ecological space may impact the reliability of the model [35,36,40–

43], the potential effect of the sampling bias in the dataset is

usually poorly taken into account or not considered at all.

However, very different SDM outputs can be generated that lead

to contrasting conclusions whether sampling bias is corrected or

not [44], making SDM studies that did not incorporate this issue

highly doubtful.

In regard to the considerable influence of sampling bias on

SDM prediction ability, Araujo et al. [45] considered the

improvement of sampling designs as one of the five major

challenges for future development of SDMs. Several bias

correcting methods have been proposed [46–51] but they have

been rarely used so far. Comparison and evaluation of different

methods to correct sampling bias have only been recently carried

out and no consensual guideline emerged to solve it. A few recent

studies explored the consequences of and potential solutions to

correct for sampling bias (by Syfert et al. [41], Kramer-Schadt

[52], Varela et al. [53] and Boria et al. [54]). In spite of their

interest, authors investigated a single case study so that it is not

possible to evaluate the efficiency of a correction method across

species. Second, the empirical bias caused by sampling intensity

[41] was never tested and no more than two correction techniques

have been evaluated at the same time whereas many more have

been proposed or used in the literature [47,49,55]. Therefore, the

influence of the nature and intensity of bias on the capacity of

various techniques to correct for sampling bias has not been

investigated. This remains however a critical issue, especially for

users who need robust and reliable SDM predictions such as

conservation practitioners.

The goal of this comparative study is to test the effect of bias

type, bias intensity, and correction method on MAXENT model

performance. Unlike the previous cited studies [41,52–54] we

assessed the performance of five bias correcting methods among

the most frequently used under various conditions of bias type and

intensity. We used a virtual species to generate four types of

sampling biases and three bias intensities, and applied on these

biased datasets different corrections. We quantified the relative

correction performance across the range of bias conditions and

across species. The same framework was also applied on two real

datasets. The full workflow on which analyses were based is

sketched in Figure 1. Therefore, the present study provides for the

first time a comprehensive multi-species evaluation of the most

common methods of sampling bias correction under different

scenarios of bias and intensities of bias. Intended for conserva-

tionists who use MAXENT on a regular basis, we expect this work

to provide insights on the selection of the most suitable methods to

produce reliable distribution models using biased datasets.

Furthermore, it encourages modelers to develop improvements

of techniques to correct for sampling bias suitable for the vast set of

modeling methods available.

Materials and Methods

Species datasetsIn order to obtain a true unbiased dataset, we created a virtual

species by randomly sampling a set of points in a given

environment determined by a single categorical variable. A similar

approach has been used formerly [52]. We extracted 2000 random

coordinates from the ‘‘Closed to open shrubland’’ category of the

North American Globcover map (Globcover 2009, http://due.

esrin.esa.int/globcover [56]) to generate an unbiased dataset. The

geographical extent of the virtual species was chosen to match the

scale of the two real species ranges which are also both located in

North America. In practice, the virtual species covered the larger

part of western North America, including the lower valleys of the

Rocky Mountains, Mojave Desert, Baja California peninsula, and

Northern Mexico (Figure 2).

We additionally used the occurrence datasets of two real species

(Figure 2). We compiled a set of 1825 occurrences for the painted

turtle (Chrysemys picta) downloaded from the World Turtle

Database (http://emys.geo.orst.edu; accessed on May 2011).

The second species was the white-spotted slimy salamander

(Plethodon cylindraceus) for which we collected a set of 208

observations. A part of the dataset was provided by J. Milanovich

and additional records were obtained from the Global Biodiversity

Information Facility (http://www.gbif.org, accessed on May

2011). According to our knowledge of the distribution of these

species, these original datasets seem relatively unbiased, i.e. the

distribution of records over space reflects the known spatial

distribution of the species.

Environmental predictorsWe used distinct sets of environmental predictors depending on

the modeled species. Climatic and topographic grids were

downloaded from the WorldClim database [32] (http://www.

worldclim.org) at a resolution of 2.5 arc-min (4.63 km at the

equator). The global map of land cover provided by the European

Spatial Agency was downloaded in its 2009 version (Globcover

2009 [56], http://due.esrin.esa.int/globcover) and rescaled to fit

the 2.5 arc-min resolution of the other variables. Finally, we

compiled 5 years of 10-day periods of NDVI (2007–2011), a

measure of vegetation productivity derived from multispectral

remote-sensing images, downloaded from the SPOT-VEGETA-

An Assessment of Methods for Correcting Sampling Bias in SDM


http://www.gbif.org

http://www.gbif.org

http://due.esrin.esa.int/globcover


http://emys.geo.orst.edu

http://www.gbif.org

http://www.worldclim.org

http://www.worldclim.org


TION project [57] (http://free.vgt.vito.be). We averaged across

these 5 years three layers of mean, minimum and maximum

annual NDVI.

We removed for each species some highly intercorrelated

(correlation coefficient computed by ArcGIS 10; .0.9 or ,20.9)

variables because multicollinearity may violate statistical assump-

tions and may alter model predictions [58]. The resulting variable

sets were composed of 14 predictors (Table 1). Since the

geographical distribution of the virtual species and Chrysemys picta

records covered a large range in North America, we modeled both

species across the same geographic area across North America.

Plethodon cylindraceus occurrences are restricted to a smaller area of

Eastern USA. Accordingly, the geographical range of predictors

was restricted to a narrower area (Table 1).

Generation of sampling biasThe three original datasets were altered to generate four types of

bias that might occur when collecting observations (Figure 3). The

original datasets were thus subsampled so that the remaining

records were biased in the geographical space. We also created

three levels of bias intensity, hereafter referred as ‘‘low’’,

‘‘medium’’ and ‘‘high’’ to assess the effect of this parameter on

model outputs (Figure 3). For each species, each combination of

bias type (4) and bias intensity (3) was replicated 10 times resulting

in a total of 360 biased datasets used to model distribution. The

four types of sampling bias were generated as follows:

(1) TWO AREAS - The original dataset was biased such that its

northern part exhibited a high density of records and the southern

part a low density. This kind of bias is common when a species is

systematically monitored in one part of its range and not surveyed

in the other, for instance in different countries or groups of

countries [44].

(2) GRADIENT - We generated a density gradient of

observations decreasing from the north to the south of the range.

This bias is close to the first one but here record density changed

gradually. Such a bias would not reflect a difference in survey

schemes between administrative divisions but a gradual reduction

of sampling intensity towards a limit of species range.

(3) CENTER - The density of occurrences gradually decreased

from the core of the distribution to the periphery. Such bias

mimics cases in which sampling effort is concentrated in the centre

of the known range of the species, whereas peripheral areas,

potentially less suitable [59], are neglected.

(4) TRAVEL TIME - We used the travel time to the nearest

city, using a map produced by the European Commission [60]

(available at bioval.jrc.ec.europa.eu/products/gam). This variable

integrates both the distance to the city and the presence of road

networks. This map was used as a grid of sampling probability, in

which probability of keeping a record was highest close to cities

and in areas with dense road networks. This bias corresponds to a

common situation where most of records are located around cities

or along roads [35,61].

The full details of the generation of sampling bias are given in

Supporting information, Material S1.

Species distribution modelingWe used for modeling the software MAXENT [30], a machine

learning algorithm that applies the principle of maximum entropy

Figure 1. Workflow used in analyses. Original datasets of a virtual and 2 real species were altered to create 12 bias combining 4 bias types and 3bias intensities. Five methods of sampling bias correction were employed to assess the improvement in the modeled distribution relative to theoriginal distribution using MAXENT. Correction performance was assessed using AUC and 3 measures of overlap between the corrected the originalunbiased model.doi:10.1371/journal.pone.0097122.g001



http://free.vgt.vito.be

to predict the potential distribution of species from presence-only

data and environmental variables [26]. Currently, this widely used

method is particularly efficient to handle complex interactions

between response and predictor variables [15,28], and is little

sensitive to small sample sizes [29]. All models were computed

using the version 3.3.3k of MAXENT (http://www.cs.princeton.

edu/,schapire/maxent/). Runs were conducted with the default

variable responses settings, and a logistic output format which

results in a map of habitat suitability of the species ranging from 0

to 1 per grid cell, wherein the average observation should be close

to 0.5 [15]. The models were evaluated by the area under the

ROC curve (AUC), and three measures of overlap with the

unbiased model (see below section ‘‘Model evaluation and

statistical analyses’’).

Methods of sampling bias correctionWe applied on all our biased datasets five methods of bias

correction that have been already published. In order to evaluate

their usefulness in real conditions, we used these methods as if the

source, shape or strength of the sampling bias was unknown.

Therefore, we did not select a correction method according to our

knowledge of the bias, as this information is unknown in most

empirical studies.

(1) Systematic Sampling. A subsample of records regularly

distributed in the geographical space was selected [46,54,55,62].

MAXENT already discards redundant records that occur in a

single cell. We removed neighboring occurrences at a coarser

resolution than MAXENT does. We created a grid of a defined

cell size and randomly sampled one occurrence per grid cell. This

subsampling reduces the spatial aggregation of records but does

not correct the lack of data due to low sampling effort in some

areas. This method could also underestimate the contribution of

suitable areas where the high density or records reflects the true

ecological value for the species. The resolution of the reference

grid was 2 degrees for Chrysemys picta and the virtual species, and

0.2 degree for Plethodon cylindraceus.

(2) Bias File. This option is implemented in MAXENT. The

software can be fed with a bias grid [49,63] that is a sampling

probability surface. The cell values reflect sampling effort and give

a weight to random background data used for modeling. An ideal

way of creating biasfiles would be to represent the actual sampling

intensity across the study area. Although it can be roughly

estimated by the aggregation of occurrences from closely related

species [48], in most real modeling situations, this information is

lacking. Thus, instead of using our knowledge of the artificially

created biases, we produced bias grids by deriving a Gaussian

kernel density map of the occurrence locations, rescaled from 1 to

20, following Elith et al. [63]. These maps were implemented in

the biasfile option in MAXENT.

(3) Restricted Background. MAXENT, as most other

presence-pseudoabsence methods, generates a ‘‘background’’ or

‘‘pseudo-absence’’ sample of points [15]. It has been argued that

the selection of background points may strongly affect the resulting

model [64–66]. By default 10000 pseudo-absences are randomly

selected from the whole rectangular study area. This approach was

followed for all the other cases, as most SDM studies keep the

default MAXENT selection of background points. However,

according to Phillips [47], if occurrences are restricted to a fraction

of the study area, model performance can be enhanced by drawing

the background points from this fraction of the area. The

reliability of predictions should be improved when the model is

transferred to the rest of the area. Following this recommendation,

we randomly sampled 10000 pseudo-absences in buffer areas

around occurrences and used them as background samples in

MAXENT. Buffer size was a radius of 500 km for the virtual

species and Chrysemys picta, and 100 km for Plethodon cylindraceus.

(4) Cluster. Biased datasets typically lead to spatial autocor-

relation of records and artificial spatial clusters of observations thus

violating the assumption of independence [67]. This bias can be

circumvented by sampling one point per cluster in environmental

space [53,68,69]. We first performed a principal component

Figure 2. Locations of records used for modeling. (A) Virtualspecies; (B) Chrysemys picta; (C) Plethodon cylindraceusdoi:10.1371/journal.pone.0097122.g002



http://www.cs.princeton.edu/~schapire/maxent/

http://www.cs.princeton.edu/~schapire/maxent/

analysis (PCA) on the environmental descriptors of occurrences

using the ‘‘ade4’’ R package [70] in order to define independent

axes in the environmental space. Then, we ran a cluster analysis

based on Euclidean distance on PCA axes space. The resulting

dendrogram was used to define a number of classes corresponding

to half of the occurrences. One record was randomly sampled per

class and the models were run on these subsampled datasets.

(5) Split. When occurrence frequency greatly differs between

two areas because of unequal sampling effort, the area can be split

in two strata within which coverage probability is more

homogeneous, and one model be computed for each stratum.

This method has been used for species occurring over a large

distribution range and extended environmental gradients

[44,51,71]. We split our biased datasets in a northern and a

southern stratum. We combined the model outputs to produce a

composite model for the entire range, keeping the highest value in

pixels where strata overlapped.

Evaluation of correction methodsTo estimate the ability of each correction method to recover the

information contained in the original unbiased data set, we used 4

criteria that correspond to the interests of different end users of

SDMs. We compared the models obtained after applying a bias in

the dataset to the original model, and after applying a sampling

bias correction method. The original dataset of the virtual species

was created to be unbiased. The model computed from it will be

thus referred as the unbiased model. Although we do not formally

know the actual bias in the Plethodon and Chrysemys original

datasets, we will also refer to the models computed from their

original datasets as unbiased models. We should keep in mind that

we compare the change in the resulting model, whatever the

original bias. The models referred as biased were computed after

applying a sampling bias and the corrected models after applying a

correction method to the biased dataset.

(1) AUC. The area under the receiver operating curve (ROC),

known as the AUC is one of the most common statistics to assess

model performance. AUC can be interpreted as the probability

that a presence cell have a higher predicted value than a absence

cell (or pseudo-absence), both of them being chosen randomly

[28]. Although the use of AUC for the evaluation of ecological

models has been criticized, especially when calculating against

background points rather than true-absences [72,73], it should be

reliable to compare models generated for a single species in the

same area and the same predictors.

The calculation of AUC was performed using the R package

‘‘PresenceAbsence’’ [74], using as test points the fraction of the

original dataset which was excluded to create the biased dataset.

The metrics was calculated by the comparison between these test

points and either (i) 10000 true absence points sampled outside the

range, which corresponds here to the true occupancy for the

virtual species, or (ii) 10000 background points randomly sampled

in all the study area for the real species. For original models, in the

absence of true test points, a mean AUC value was computed

Table 1. Environmental predictors included in MAXENT modeling for the virtual species, Chrysmeys picta and Plethodoncylindraceus.

Virtual species Chrysemys picta Plethodon cylindraceus

Variable

Altitude 6 6 6

Annual mean temperature 6 6 6

Mean diurnal range 6 6 6

Isothermality 6 6 6

Temperature annual range 6 6 6

Mean temperature of wettest quarter 6 6 6

Annual precipitation 6 6 6

Precipitation seasonality 6 6 6

Precipitation of warmest quarter 6 6 6

Precipitation of coldest quarter 6 6 6

Land cover 6 6 6

Maximum NDVI 6 6

Mean NDVI 6 6 6

Minimum NDVI 6 6 6

Mean temperature of driest quarter 6

Extent

Longitude

min 2140.00 2140.00 288.63

max 250.00 250.00 270.68

Latitude

min 20.00 20.00 28.91

max 75.00 75.00 45.46

The selected layers are indicated for each species, as well as the extent of modeling (in decimal degrees).doi:10.1371/journal.pone.0097122.t001



using 5 random splits of the dataset, each subsample being used in

turn to evaluate the model.

(2) DGEO overlap in the geographical space. Several

metrics of niche overlap are available (e.g. D [75], modified

Hellinger distance I [76] or BC [77]). We used the Schoener’s D

index [75] that has been suggested to be best suited for SDM

outputs [78]. This statistics considers the probability distributions

across space of the difference in the probability of presence of two

species, based on their respective distribution models. Dgeo index is

ranged from 0 (no overlap) to 1 (complete overlap, identical

models).

(3) DENV overlap in the environmental space. We

estimated niche overlap in the environmental space between the

unbiased, biased, and corrected models. We used the PCA-env

approach described by Broennimann [79] to calculate Schoener’s

D index based on the environmental characteristics of two sets of

occurrences. This approach defines the environmental space by

the two first axes of a principal component analysis of all the pixels

of the study area. The niche overlap is calculated from the

smoothed density of occurrences in the environmental space

following a kernel density function applied on each dataset.

Depending on the correction method used, some models can be

based on the same input dataset (e.g. the biasfile correction uses the

same records as the biased model). In order to compare our

SDMs, we applied the PCA-env method on 500 points sampled

from the SDM outputs instead of on the input records. We

selected these points in the output map using the SDM probability

of presence as a sampling probability.

(4) GOVER overlap between binary maps. SDM outputs

are often converted to binary maps that are more tractable for

conservationists who for instance need to delineate protected

areas. In such maps, a pixel is considered as either suitable to the

species or not. We used the non-fixed 10th percentile training

presence threshold value to generate binary maps as proposed by

Liu et al. [80]. We then measured the overlap between biased and

corrected models, and unbiased models. This measure strictly

measures the geographical overlap whereas the D index estimates

the overlap of ecological niches in environmental space (Denv) or

projected onto the geographical space (Dgeo).

To evaluate the performance of bias correction, we derived new

indicators from AUC, Dgeo, Denv, and Gover that quantify the

improvement of the corrected model to the biased model,

standardized by the difference between the unbiased and the

biased models. These indices, named respectively DAUC, DDgeo,

DGover and DDenv were calculated as follows:

DAUC~ AUCcorrected{AUCbiasedð Þ= AUCunbiased{AUCbiasedð Þ

DDgeo~ Dgeocorrected{Dgeobiased

� �.1{Dgeobiased

� �

DGgover~ Govercorrected{Goverbiased

� �.1{Goverbiased

� �

DDenv~ Denvcorrected{Denvbiased

� �.1{Denvbiased

� �

These four indices range from -‘ to 1, a positive value

indicating that the model was actually corrected (with 1

corresponding to perfect correction, i.e. corrected model exactly

similar as the unbiased one) whereas a negative value indicates

that the correction produced a worse model than the biased one.

Results

Effect of bias type and intensity on model outputsThe biased models resulted in a reduction of AUC in all cases

and a deviation from the unbiased model for all overlap measures

(Figure 4). The deviation varied largely depending on species and

bias type though: 0.28–0.91 for Dgeo, 0.18–0.89 for Denv, 0.03–1 for

and Gover. For the virtual species, the bias type yielding the largest

deviation depended on the performance measures considered: ‘‘2

areas’’ for the AUC, ‘‘travel time’’ for Dgeo, ‘‘Center’’ for Denv and

‘‘Gradient’’ for Gover, the latter providing the lowest values of

overlap with the original unbiased models. However, the

differences between unbiased and biased models remained

moderate (mean percentage variation: AUC: 21.74%; Dgeo: 2

24.41%; Denv: 224.62%; Gover: 230.07%). All bias types had also

globally similar effects in terms of deviation from the unbiased

model (Figure 4). For Chrysemys picta, all evaluation measures were

strongly affected by the ‘‘center’’ bias. AUC decreased more than

5%, and overlaps with the unbiased model ranged from 0.26 to

0.49. In contrast, the P. cylindraceus dataset was overall weakly

affected by the biases so that the biased models did not lead to

Figure 3. Generation of sampling bias for the virtual species. Togenerate artificial sampling bias, the original dataset (here the virtualspecies) was altered into 4 different types of bias (rows), each with 3intensities (columns).doi:10.1371/journal.pone.0097122.g003



noticeable differences with the unbiased model. The strong effect

of the ‘‘center’’ bias was visible in Plethodon cylindraceus only for the

overlap of binary maps (Gover). This bias in which only the central

zone is sampled may exclude a large part of the original

environmental space and lead to very inaccurate SDM outputs.

Interestingly, the decrease in AUC performance for all bias types

was more pronounced in C. picta than the two other datasets even

when the values of overlap were in the same range.

Relative performance of correction methodSince we evaluated the performance of correction methods

using indices with different sets of assumptions, interpretation may

slightly differ with the measure considered. However, as we mainly

aimed at comparing SDM outputs, i.e. maps of habitat suitability,

we primarily focused our interpretations on DDgeo which truly

evaluates the overlap between standard SDM maps. Moreover,

the two measures based on Schoener’s D, in geographic (DDgeo)

and in environmental space (DDenv), were highly correlated and

outputs of bias correction were qualitatively similar (Supporting

information, Figure S1). We discuss here results for DDgeo only.

Correction performance strongly depended on the species

(Table 2). Considering the three species together, less than half

(29%) of all combinations (species 6 bias type 6 bias intensity 6correction method) yielded corrected models (following DDgeo) with

more accurate predictions than the biased model. For the virtual

species, and considering DDgeo, 57% of corrected models (34 out of

60 combinations of bias type, bias intensity and correction

method) were more similar to the model generated with the

unbiased dataset than the biased model (Table 2). Most cases for

which no method was able to provide bias correction were

‘‘center’’ and ‘‘travel time’’ biases, with medium to high intensities.

Conversely, only 7% of P. cylindraceus models were corrected (4

cases out of 60), while 25% of C. picta models were corrected (15

cases out of 60) and offered a better result than the biased model.

Regardless of the species, the bias type, and the metrics

considered, the restricted background method failed to improve

the biased models in almost all tested cases. The other methods

performed better but were ranked differently depending on bias

type. Systematic sampling performed slightly better and more

consistently among the competing methods as shown by the

relative performance of each method across bias types (Figure 5).

Although systematic sampling was not always ranked first, it

showed very little deviation from the most performing method and

performed on average better than the others (for DDgeo: mean rank

Systematic sampling = 2.1161.08 SD; mean rank Split = 2.5361.08

SD, mean rank Cluster = 2.61361.23 SD; mean rank Biasfile

= 3.3161. 31 SD). In contrast, the restricted background method

recorded the least correction (mean rank Restricted background

= 4.4461.13 SD).

Overall, and considering only DDgeo, the systematic sampling

method was able to correct the bias (DDgeo.0) in 33% of the test

cases. This success rate rose to 66% in the case of the virtual

species, for which we were able to compare to a true unbiased

model. However, the biasfile corrected the initial bias in 23% of

test cases. The cluster and split method were both efficient in 23%

of cases while only 6% of cases were corrected by the restricted

background method.

Interestingly, relative performance between methods was

consistent across metrics (Figure 5). The restricted background

method was always the least performing one in terms of DAUC,

Figure 4. Evaluation indices of biased models across bias intensities. Reduction of AUC between unbiased and biased models (inpercentage), Schoener’s D overlaps between biased and unbiased models computed on SDMs (Dgeo) and in environmental space (Denv), and Gover thebinary distribution overlap (mean 6 SD). Dark grey bars: Chrysemys picta, light grey bars: Plethodon cylindraceus, black bars: virtual species.doi:10.1371/journal.pone.0097122.g004



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DDgeo and DGover (but for C. picta and DDgeo, for which it is ranked

4/5). The systematic sampling method was among the most

performing methods. However, even if systematic sampling was

overall the most efficient method across species in terms of DDgeo, it

was outperformed by the split or biasfile methods in some cases for

the virtual species, or by the cluster method under some

combinations of bias 6 intensity for the two real species

(Table 2). However, when the systematic sampling was unable to

resolve the bias, this latter was most often equally poorly corrected

by any of the methods tested.

Discussion

As an unexpected first finding, we noticed that the range of

AUC values obtained for biased and corrected models remained

high even for models with the strongest biases. The decrease in

AUC observed after applying the bias was moderate, less than 2%

on average, across species and bias type. Moreover, the AUC

values of the biased models were almost always over 0.8 or 0.9,

which would classify the models as ‘‘good’’ or ‘‘very good’’ (Araujo

et al. [81] adapted from Swets [82]). Together with other studies

[72,73,83] our results highlight that this measure may poorly

reflect model accuracy. Therefore, studies that focus solely on the

AUC value should interpret their results with caution. AUC may

be a good statistical measure of discrimination ability, but it often

fails to quantify the ecological realism of modeled distribution

[72,73,83] especially when estimated from presence-only data.

Because we have a reference model, we will mainly focus on the

overlap indices with the unbiased model as a measure of predictive

accuracy performance.

Contrary to previous studies investigating sampling bias

correction in SDM that focused on a few methods and simple

biases [41,52–54], we reviewed here five different ways to deal

with sampling bias and used both real and virtual datasets under

various bias scenarios. We also considered bias intensity that has

been to our knowledge never assessed and proved to be of as a

high concern as the type of bias. Moreover, instead of relying only

on classical measures of SDM performance such as AUC (as used

in Syfert et al. [41], Varela et al. [53] and Boria et al; [54]) or

omission/commission error (as used in Kramer-Schadt et al. [52]),

we evaluated the correction performance by directly comparing

the SDM outputs. Therefore, we actually assessed the ability of the

tested methods to recover the unbiased model, which is the

expected behavior of an efficient sampling bias correction. In

addition, rather than basing our conclusions on island species

[41,52,54], we used continental species whose distributions are

clearly shaped by climate and not by a geographically bound

space.

Our results clearly evidence that the different methods of

sampling bias correction tested here may have very variable

efficiency depending on the modeling conditions (biases type and

correction method). Interestingly, the correction may have a

positive effect, and actually contributes to correct the bias;

nonetheless, in some cases it may produce a poorest model than

the biased model. These results suggest that the problem of

sampling bias in species distribution modeling has probably

multiple answers depending on the context. We especially

emphasize that the type and intensity of bias influence the ability

of various methods to resolve the initial bias.

However, correction methods did not perform equally across

the various conditions. The less efficient method restricted the

spatial extent of the background whereas in other methods, the

background points were selected from the whole available

environment (i.e. randomly drawn from the area covered by the

environmental grid files). Surprisingly, this method is often used

and have been contributed to improve SDM performance in some

cases [47,48]. However, as suggested by Thuiller et al. [84] and

Vanderwal et al. [85], excessively restricting the geographical

extent of pseudo-absences to a narrow area or selecting them from

a too large area reduces model accuracy. Background selection

may greatly influence the resulting model as it determines the

underlying assumptions of the model to use [64]. Therefore, this

step should be undertaken with caution. The size of the buffer used

for background selection also greatly influences model perfor-

Figure 5. Rank of each method to correct sampling bias. Mean ranks 6 standard-error for the performance of each method to correctsampling bias for each species (Chrysemys picta: left, Plethodon cylindraceus: center, virtual species: right), following 3 measures of correctionperformance: DAUC (left), DDgeo (centre), and DGover (right). For each type of bias and bias intensity, the method which results in the most efficientcorrection is set to 1 whereas the least powerful method is set to 5. The plotted values are the mean rank across the 4 types of bias and 3 intensities.doi:10.1371/journal.pone.0097122.g005



mance. For instance, AUC often increases with the size of the

study area because it contributes to include background points that

have environmental characteristics greatly distant from the species

requirement, resulting in artificial increase of SDM validation

[65]. The selection of the training area should therefore be strictly

relevant to the ecology of the species and the objective of the study.

A relevant selection of the training area (the geographic region in

which background points are selected) should reflect the

geographical space accessible to the species over a given time

period [65]. It may thus be essential to carry out a rigorous

investigation of the optimal geographic distance between the set of

occurrences used to train the model and background points. It has

to be both optimal for model training and biologically meaningful.

The interpretation of the modeled distribution must also be

engaged carefully as it may reflect the fundamental niche or the

true occupied range, and often a position between both.

Regarding the high variability in correction performance of the

different methods depending on various factors, it is difficult to

propose a universal guideline to solving sampling bias. It might be

advisable to evaluate first several types of correction. The final

choice of correction method would be then based on their effect in

classical SDM evaluation metrics (e.g. AUC, Kappa, True Skill

Statistics TSS) and possibly the adequacy of output maps to a priori

knowledge of the species distribution. A first useful step might also

be to evaluate bias type to design and select the most appropriate

correction. For instance, the split method makes sense only if the

most and less sampled areas are at least roughly known. Most of

the time, sampling bias is only inferred by the known sampling

effort or empirical knowledge of the species distribution. The true

severity and shape of this bias is almost always lacking. However,

in some cases, bias can be evaluated by comparing the geographic

distribution of the available occurrences to known sources of bias.

An estimation of sampling probabilities across the study area can

provide insights on the potential bias that may affect the collected

observations and help in further choice of the correction method.

The known characteristics of the modeled species may also

condition the strategy to use. A species with an expected very large

geographical and/or environmental range should benefit from

being split into two or more partitions that are combined

afterward [51]. Finally, the five methods tested here are not

necessarily exclusive. For instance, it is possible to split a large

dataset and apply systematic sampling to each dataset in species

with broad distributions [44] or to apply the biasfile method after

using first another correction method

Nevertheless, we found that only systematic sampling constantly

performed well irrespective of species and bias type. Interestingly

enough, it happened to be the simplest and most obvious way to

solve the geographic bias. Beside, this method can be quickly

applied to any dataset, even if the nature of the bias is unknown.

Kramer-Schadt et al. [52] and Boria et al. [54] also identified this

technique, which they named spatial filtering, as the most effective

(but note that Varela et al. [53] found that environmental filtering,

equivalent to our cluster method, may provide better results). We

might keep in mind that this method may have a few drawbacks

though. Subsampling the complete dataset may alter the

distribution of occurrences in the environmental space and

exclude some portion of environmental space from the input

records. This problem may be circumvented by adjusting the grid

size but this may not be possible when the sample size of

occurrences (presences) is too low. On the contrary, smoothing the

distribution of occurrences may lead to overestimating the

probability presence in marginal areas. The grid cell size used to

sample the occurrences may also be a source of problem; it must

be large enough to resolve the bias but not too large to result in a

strong loss in resolution. A fine adjustment of the parameters of the

method (e.g. the resolution of systematic sampling that provides the

optimal trade-off between sampling bias correction and informa-

tion reduction) is thus necessary to maximize its performance.

Our results suggest that the difference in performance between

the systematic sampling method and the optimal method for the

dataset under investigation is slight. Since systematic sampling

seems to be robust enough to differentiate sampling bias and

species, we suggest that this could be the method selected first if no

further attempts to correct sampling bias are to be made. This

method provides a quick and efficient way to improve SDM from

a biased dataset and is likely to be relevant most of the time. Even

if the elaboration of a step-by-step framework would be ideal to

assist in the definition of a reliable strategy of bias correction, we

highlight that most SDMs studies, at least those that use

MAXENT as modeling algorithm, would highly benefit from this

simple tweaking of input occurrences. Regarding the major

impacts that conservation actions are expected to provide

[86,87], they must be based as much as possible on irrefutable

models. Therefore, it is essential to develop simple methods

intended for conservation practitioners, such as techniques of

sampling bias correction, to build robust distribution models. In

this regard, we encourage MAXENT users to carefully take

sampling bias into account, and to use systematic sampling of their

input occurrences as a quick and simple resolution of bias.

Supporting Information

Figure S1 Correlations between measures of correctionperformance.

(PDF)

Material S1 Details of the generation of sampling bias.

(PDF)

Author Contributions

Conceived and designed the experiments: YF JOE DR JS. Analyzed the

data: YF. Wrote the paper: YF JS.

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